What is the name for the operation from mappings $f:X\to Y_1$ and $g:X\to Y_2$ with the same domain to mapping $h:X\to Y_1 \times Y_2$ defined as $h(x)=[f(x), g(x)]$? I named it pairing, but it is unlikely others will call it the same way.

3 Answers
3

It appear clear that $h(x) = [f(x),g(x)]$ should probably be written: $h(x) = \left(f(x), g(x)\right)$ - and called an ordered pair, with range being the "ordered" Cartesian product of the ranges/images of the two functions involved.

In the general case, we'd have an ordered "$n$-tuple", where $n$ denotes the number of "arguments" (in this case, the number of functions whose "ranges"/"images" are factors in cross product to which $h$ is mapping) or in your notation, $n = |I|$.

ADDED to address comment below:

There is no operation from f, g to h, rather, there is an operation h defined in terms of f and g:

I think I understand the operation on mappings is defined in terms of the operation on sets. I know the name of the operation on sets. Just wonder if there is a name for the operation on mappings.
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TimFeb 1 '13 at 18:35